TY  - JOUR
A1  - König, Christoph
A1  - Spoden, Christian
A1  - Frey, Andreas
T1  - An optimized Bayesian hierarchical two-parameter logistic model for small-sample item calibration
T2  - Applied psychological measurement
N2  - Accurate item calibration in models of item response theory (IRT) requires rather large samples. For instance, N > 500 respondents are typically recommended for the two-parameter logistic (2PL) model. Hence, this model is considered a large-scale application, and its use in small-sample contexts is limited. Hierarchical Bayesian approaches are frequently proposed to reduce the sample size requirements of the 2PL. This study compared the small-sample performance of an optimized Bayesian hierarchical 2PL (H2PL) model to its standard inverse Wishart specification, its nonhierarchical counterpart, and both unweighted and weighted least squares estimators (ULSMV and WLSMV) in terms of sampling efficiency and accuracy of estimation of the item parameters and their variance components. To alleviate shortcomings of hierarchical models, the optimized H2PL (a) was reparametrized to simplify the sampling process, (b) a strategy was used to separate item parameter covariances and their variance components, and (c) the variance components were given Cauchy and exponential hyperprior distributions. Results show that when combining these elements in the optimized H2PL, accurate item parameter estimates and trait scores are obtained even in sample sizes as small as N = 100. This indicates that the 2PL can also be applied to smaller sample sizes encountered in practice. The results of this study are discussed in the context of a recently proposed multiple imputation method to account for item calibration error in trait estimation.
KW  - Bayesian
KW  - hierarchical models
KW  - item response theory
KW  - calibration
KW  - simulation
KW  - small samples
Y1  - 2019
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/54836
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-548369
SN  - 1552-3497
SN  - 0146-6216
VL  - 44
IS  - 4
SP  - 311
EP  - 326
PB  - SAGE Publications
CY  - London
ER  -